Polarization dependent loss (PDL), in which optical power transmitted along a propagation path changes as a function of polarization state of the light beam, is a well-known phenomenon in optical systems and instruments, for example optical spectrum analyzers. The maximum difference in power over all possible polarization states is termed polarization dependent loss (PDL). Because changes in polarization state of an input beam occur at an unpredictable time and rate, the optical spectrum analyzer (OSA) or other instrument preferably uses some type of static PDL correction that is not dependent on time or the exact state of polarization of the light that enters the system.
FIG. 1 illustrates schematically a current Agilent Technologies 8614x series OSA instrument (see Agilent Technologies data sheet 8614xB Optical Spectrum Analyzer Family Technical Specifications). This instrument incorporates a monochromator 10 having diffraction grating 17 as a dispersive element. An input beam 12a typically entering through input fiber 11 is directed by first mirror 13a and second mirror 13b through collimating element 16 along two passes 12a and 12c onto diffraction grating 17. Between the two passes, the beam is directed through a resolution defining aperture that is normally incorporated into slit wheel 14 to provide a range of aperture sizes. Collimating element 16, typically a lens, refocuses diffracted light from the surface of grating 17 in each pass 12b and 12d back onto the optical plane of slit wheel 14. Output beam 12e is deflected by output mirror 13c into output fiber 18.
The current method used to reduce PDL induced changes in power measured by the OSA as the input light source polarization state changes is to rotate the state of polarization of the input beam through monochromator 10 by 90 degrees between the first pass and the second pass. In the current instrument, this is implemented by inserting half-wave plate 15 in second pass 12c immediately after reflection from second mirror 13b. This balancing technique effectively rotates the S and P states of polarization, which by definition are orthogonal, and reverses their state between first pass 12a, 12b and second pass 12c, 12d through the optical system. Any arbitrary state of polarization can be made up of a superposition of the orthogonal S and P states. For example, if the input beam state were S, after traveling through the first pass of the instrument it would be rotated to the orthogonal state P, and vice versa. Rotating the states so that both orthogonal states exist in the double-pass system regardless of the input state means that the output power of the OSA ideally does not change, even though the input polarization state changes. For this technique to work most effectively, the net reflectance for S polarization on first pass 12a, 12b multiplied by the net reflectance for P polarization on second pass 12c, 12d equals the net reflectance of P polarization on first pass 12a, 12b multiplied by the net reflectance for S polarization on second pass 12c, 12d. Orthogonal states S and P are used to analyze this system because they are additionally the worst case states for this system.
To determine the power that is transmitted through the optical spectrum analyzer for the two worst case polarization states the following relation may be used.Power out=Power In*Tiinput fiber*Ri grating*Ri mirror1*Ri mirror2*Ri′ grating*Ri′ mirror3*Ti′ output_fiber
In this expression, R and T represent respective reflection and transmission percentages, subscript i represents the polarization state, e.g., S or P, at the specified surface, and subscript i′ represents the rotated polarization state as the beam propagates from the first pass to the second. Because each surface has a different orientation, what would be considered S for one surface could be P for another, so to remove any misunderstanding, the rule applied in the following discussion is that the input polarization state is identified relative to the grating surface. Referring to the coordinate axes in FIG. 1, the grating dispersion direction and the P polarization direction are parallel to the y-axis, which is perpendicular to the plane of the figure, whereas the non-dispersion direction and the S polarization direction are parallel to the x-axis, pointing upward parallel to the plane of the figure. Both polarizations are mutually perpendicular to the z-axis, which is essentially parallel to the dominant propagation direction of light beam passes 12a, 12b, 12c, and 12d. Because any polarization state or unpolarized state of the field can be represented as a superposition of the orthogonal basis set of S and P, which also happen to be the worst case polarization states, only these two electric field states are required to define the worst case polarization dependent loss. The following example uses common reflectance values and an input power of one milliwatt.
P input state (P relative to Grating)= 1.0 mW*0.964*0.5*0.986*0.986*0.8*0.992*0.95first passsecond pass= 0.4686*0.754= 0.353 mWS input state (S relative to Grating)= 1.0 mW*0.966*0.8*0.992*0.992*0.49*0.986*0.94first passsecond pass= 0.7604*0.454= 0.345 mW
This example shows that for the first pass with a P input state the net output power is 0.4686 mW. For the second pass with an S input state, which is actually P relative to the grating having had the polarization rotated by half-waveplate 15, the net power is 0.454 mW. This shows that the net effects of the two halves of the optical spectrum analyzer are closely but not perfectly balanced. If the first pass with an S input state were compared to the second pass with a P input state, the same result occurs. If these passes are multiplied together, both input states will result in roughly the same power through the optical spectrum analyzer at approximately 0.35 mW. The transmitted powers are not exactly the same for the two different polarization states. In this example, the net system PDL is defined by the relation, PDL=10*LOG(Power for P input state/Power for S input state), which in this example evaluates to slightly less than 0.1 dB polarization dependent loss. If great care is not taken in the selection of the optical system components this value for PDL can be as large as 1 dB.
These differences are important, because the input polarization changes continually and unpredictably with time, due for example to fluctuations in optical source and/or fiber polarization states. These can produce instrument output power fluctuations that may be incorrectly attributed, for example, to source power fluctuations, but in reality may be artifacts produced by instrument PDL. It would therefore be advantageous for an optical system or instrument to be substantially immune to performance changes arising from input polarization fluctuations.